Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}2x+4y &= -6 \\ -7x-5y &= 8\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $-7x = 5y+8$ Divide both sides by $-7$ to isolate $x$ $x = {-\dfrac{5}{7}y - \dfrac{8}{7}}$ Substitute this expression for $x$ in the first equation. $2({-\dfrac{5}{7}y - \dfrac{8}{7}}) + 4y = -6$ $-\dfrac{10}{7}y - \dfrac{16}{7} + 4y = -6$ Simplify by combining terms, then solve for $y$ $\dfrac{18}{7}y - \dfrac{16}{7} = -6$ $\dfrac{18}{7}y = -\dfrac{26}{7}$ $y = -\dfrac{13}{9}$ Substitute $-\dfrac{13}{9}$ for $y$ in the top equation. $2x+4( -\dfrac{13}{9}) = -6$ $2x-\dfrac{52}{9} = -6$ $2x = -\dfrac{2}{9}$ $x = -\dfrac{1}{9}$ The solution is $\enspace x = -\dfrac{1}{9}, \enspace y = -\dfrac{13}{9}$.